The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  2  4  1  1  1  4  1  2  1  1  1  1  2  2  4  2  4  2  1
 0 12  0  4  0  0  4 12  0  0 12 12  0  8 12 12  0  4 12 12  4  8  8 12  4  8  8  4  8 12  4  4 12  4 12  8  0  4  0  4  4  8  0
 0  0 12  4  0 12  4  0  0 12 12  8  8 12  4  0  8  4 12  0  4  4 12  0  4  4  4  0  0  8  0  4  0 12 12  8 12  4 12 12  4  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  8  0  0  8  8  0  8  8  8  8  8  0  0  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  0  8  0  0  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  0  0  0  8  0  8  8  8  0  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  0  8  0  0  0  0  8  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  8  0  0  0  8  8  0  0  8  0  0  0  8  0  8  8  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  8  0  0  0  8  0  8  8  0  8  8  8  0  0  8  0  8  8  0  8  8  0  0  8  8  8  8
 0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  8  8  0

generates a code of length 43 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+78x^32+52x^33+140x^34+186x^35+351x^36+358x^37+592x^38+816x^39+2226x^40+2652x^41+4806x^42+8196x^43+4803x^44+2684x^45+2236x^46+912x^47+612x^48+348x^49+336x^50+114x^51+109x^52+46x^53+64x^54+16x^55+10x^56+4x^57+14x^58+1x^60+4x^62+1x^64

The gray image is a code over GF(2) with n=344, k=15 and d=128.
This code was found by Heurico 1.16 in 14.8 seconds.